Nozzle for low pressure flash tanks for ore slurry

ABSTRACT

A wear-resistant flash tank pressure let down nozzle for use in passing an ore slurry into an ore slurry flash tank to release steam from the slurry and reduce the pressure of the slurry. The nozzle has an expansion cone flaring toward the discharge end of the nozzle. The cross-sectional area of a choke section of the nozzle and the exit diameter of the expansion cone are selected to establish a relationship between pressure upstream of the nozzle and pressure in the flash tank so that underflashing, overflashing, and shock waves inside the flash tank are minimized.

RELATED U.S. APPLICATION DATA

This is a continuation of Application Ser. No. 09/061,956, filed on Apr.17, 1998, now U.S. Pat. No. 6,110,255.

BACKGROUND OF THE INVENTION

This invention relates to the release of pressure from oxidized oreslurry in an autoclave circuit. In particular, the invention relates tothe design of a nozzle system through which ore slurry passes intoslurry flash tanks.

Autoclave circuits are used to recover gold from refractory sulfidicores. Ore leaving an autoclave is typically passed to a series of flashtanks where pressure is let down and steam is flashed off to cool theslurry, and reduce it to atmospheric pressure for further processing.Steam from each flash tank is recycled and contacted with autoclave feedslurry in a complementary splash condenser, operated at substantiallythe same pressure as the flash tank, for preheating the autoclave orefeed slurry. In one particular system the pressure from the autoclaveslurry discharge is let down in two stages. In the first stage, pressureis let down from about 420 psig to about 120 psig. In the second stage,pressure is let down from about 120 psig to atmospheric. This secondpressure drop corresponds to a much greater volume expansion than in thefirst stage.

Heretofore this second pressure drop from about 120 psig to atmospherichas been accomplished by use of a nozzle system comprising a straighttubular choke extending from outside the flash tank to inside the flashtank. The choke was surrounded by a ceramic lined blast tube extendingfurther into to flash tank, as shown in FIG. 4. As the volume of theslurry expands rapidly upon passage through the choke, the blast tubewas violently impacted with steam entrained with ore slurry.Catastrophic failure of the blast tube, resulting in ore slurry damagingand even breaching the low pressure flash tank, has occurred. Thetypical life of such nozzle systems, and in particular of the blasttubes, has been relatively short, for example, six weeks, depending onoperating parameters, ore characteristics, and many other factors.Rebuilding and/or replacing such nozzle assemblies is expensive in termsof capital costs and in terms of process downtime.

SUMMARY OF THE INVENTION

Among the several objects of the invention, therefore, are the provisionof an extended life nozzle system for a low pressure slurry flash tank;the provision of an improved apparatus for preheating gold ore slurryprior to pressure oxidation and for reducing the pressure of pressureoxidized gold ore slurry after pressure oxidation; and the provision ofan improved process for reducing the pressure of pressure oxidized goldslurry.

Briefly, therefore, the invention is directed to a wear-resistant flashtank pressure let down nozzle for use in passing an ore slurry into anore slurry flash tank to release steam from the slurry and reduce thepressure of the slurry. The nozzle has an inlet end, a discharge end,and a tubular passageway extending therebetween for passage of theslurry from a location outside the flash tank in fluid flowcommunication with the inlet end. The slurry passageway has a chokecomprising a zone of the passageway in which its cross sectional area issmallest, the passageway flaring with respect to the axis thereof towardthe discharge end to define an expansion cone. The cross-sectional areaof the choke and the exit diameter of the expansion cone being selectedto establish a relationship between pressure upstream of the nozzle andpressure in the flash tank so that shock waves inside the flash tank areweaker than shock waves inside a reference flash tank having identicaldimensions and configuration and operating under identical conditionsexcept having a reference pressure let down nozzle consisting of astraight choke.

The invention is also directed to an ore slurry flash tank apparatus forreceiving and holding pressure oxidized ore slurry for reducing thepressure of pressure oxidized gold ore slurry. The apparatus has avessel having a bottom, a top, and side walls, and a wear-resistantflash tank pressure let down nozzle. The nozzle has an inlet end, adischarge end, and a tubular passageway extending therebetween forpassage of the slurry from a location outside the flash tank in fluidflow communication with the inlet end. The slurry passageway has a chokecomprising a zone of the passageway in which its cross sectional area issmallest, the passageway flaring with respect to the axis thereof towardthe discharge end to define an expansion cone. The cross-sectional areaof the choke and the exit diameter of the expansion cone are selected toestablish a relationship between pressure upstream of the nozzle andpressure in the flash tank so that shock waves inside the flash tank areweaker than shock waves inside a reference flash tank having identicaldimensions and configuration and operating under identical conditionsexcept having a reference pressure let down nozzle consisting of astraight choke.

In another aspect, the invention is directed to an apparatus forpreheating gold ore slurry prior to pressure oxidation and for reducingthe pressure of pressure oxidized gold ore slurry after pressureoxidation. There is a flash tank for receiving a volume of pressureoxidized gold ore slurry, the flash tank comprising a vessel having abottom, a top, and side walls, and a nozzle on the top of the vessel forpassing ore slurry into the vessel. The nozzle has an inlet end, adischarge end, and a tubular passageway extending therebetween forpassage of the slurry from a location outside the flash tank in fluidflow communication with the inlet end. The slurry passageway has a chokecomprising a zone of the passageway in which its cross sectional area issmallest, the passageway flaring with respect to the axis thereof towardthe discharge end to define an expansion cone. The cross-sectional areaof the choke and the exit diameter of the expansion cone are selected toestablish a relationship between pressure upstream of the nozzle andpressure in the flash tank so that shock waves inside the flash tank areweaker than shock waves inside a reference flash tank having identicaldimensions and configuration and operating under identical conditionsexcept having a reference pressure let down nozzle consisting of astraight choke. There is a steam outlet for passing steam out of theflash tank, and a splash condenser for contacting ore slurry with steamprior to pressure oxidation of the ore slurry in order to preheat theore slurry, the splash condenser having a steam inlet. There is alsoconduit for transferring steam from the steam outlet of the flash tankto the splash condenser.

The invention is further directed to a process for reducing the pressureof pressure oxidized ore slurry from above about 100 psig to aboutatmospheric. Slurry is passed through a nozzle into a flash tank, thenozzle disposed on the top of the flash tank and comprising a receivingend and a discharge end, and a slurry passageway extending through thenozzle from the receiving end to the discharge end for passage of theslurry into the flash tank from a location outside the flash tank. Theslurry passageway flares outwardly at an angle of about 15° toward thedischarge end to gradually reduce the pressure of the slurry and todirect the slurry such that it impacts a volume of slurry in the bottomof the flash tank.

The invention is also directed to an ore slurry flash tank apparatus forreceiving and holding pressure oxidized ore slurry for reducing thepressure of pressure oxidized gold ore slurry. There is a vessel havinga bottom, a top, and side walls, and a nozzle on the top of the vesselfor passing ore slurry into the vessel. The nozzle has an inlet end, adischarge end, and a tubular passageway extending therebetween forpassage of the slurry from a location outside the flash tank in fluidflow communication with the inlet end. The slurry passageway comprises achoke comprising a zone of the passageway in which its cross sectionalarea is smallest, the passageway flaring with respect to the axisthereof toward the discharge end to define an expansion cone. The nozzlehas a choke diameter of between about 3½ and about 4½ inches, anexpansion cone exit diameter of between about 7 and about 7½ inches, andan expansion cone length of between about 5¾ inches and about 6¾ inches,to establish a relationship between pressure upstream of the nozzle andpressure in the flash tank so that shock waves inside the flash tank areweaker than shock waves inside a reference flash tank operating underidentical conditions except having a reference pressure let down nozzlecomprising a straight choke.

In another aspect, the invention is directed to an ore slurry flash tankapparatus for receiving and holding pressure oxidized ore slurry forreducing the pressure of pressure oxidized gold ore slurry from betweenabout 100 psig and about 140 psig to about atmospheric. There is avessel having a bottom, a top, and side walls, and a nozzle on the topof the vessel for passing ore slurry into the vessel. The nozzle has atubular passageway extending therebetween for passage of the slurry froma location outside the flash tank in fluid flow communication with theinlet end, the slurry passageway comprising a choke comprising a zone ofthe passageway in which its cross sectional area is smallest. Thepassageway flares with respect to the axis thereof toward the dischargeend to define an expansion cone. The nozzle has a choke diameter ofbetween about 3.8 and about 4.1 inches corresponding to the smallestcross-section in the slurry passageway, the straight section having alength of between about 9½ and about 10½ inches, an expansion cone exitdiameter of between about 7.1 and about 7.4 inches, an expansion conelength of between about 6 inches and about 6.2 inches, and an expansioncone length of between about 14° and about 16°, to establish arelationship between pressure upstream of the nozzle and pressure in theflash tank so that shock waves inside the flash tank are weaker thanshock waves inside a reference flash tank operating under identicalconditions except having a reference pressure let down nozzle comprisinga straight choke.

Other objects and features of the invention will be in part apparent andin part pointed out hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowsheet of a gold recovery operation in which theinvention is used;

FIG. 2 is a more detailed flowsheet of part of the gold recoveryoperation of FIG. 1;

FIG. 3 is a more detailed flowsheet of a second part of the goldrecovery operation of FIG. 1;

FIG. 4 is a front sectional schematic view of a prior art low pressureflash tank nozzle assembly installed in a flash tank;

FIG. 5 is a more detailed front sectional view of a prior art lowpressure flash tank nozzle assembly having a straight choke;

FIG. 6 is a front sectional schematic view of the low pressure flashtank nozzle of the invention installed in a flash tank;

FIG. 7 is a more detailed front sectional view of the nozzle of theinvention;

FIG. 8 is a perspective view of the nozzle of the invention;

FIG. 9 is a top view of the nozzle of the invention;

FIG. 10 is a bottom view of the nozzle of the invention;

FIG. 11 is a graph depicting optimum design for a low-pressure flashnozzle; and

FIG. 12 is a graph depicting kinetic power due to steam expansion.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 illustrates a preferred gold recovery process in which theinvention is used. This process is described generally in Thomas et al.U.S. Pat. No. 5,071,477 and Thomas et al. U.S. Pat. No. 5,489,326, theentire disclosures of which are expressly incorporated by reference.According to such a process, ore is crushed and wet milled, and theground ore slurry screened for trash or tramp material. The ground oreis thickened by removal of excess water in a solid-liquid separationoperation. The ore slurry is then subjected to pressure oxidation in thepresence of sulfuric acid using oxygen gas at elevated pressure. It issometimes necessary to add sulfuric acid to facilitate oxidation, so theaddition of sulfuric acid to the thickened ore slurry is indicated as anoptional step. Pressure oxidation is typically conducted in a horizontalmulti-compartmented autoclave, the compartments of which are preferablyof substantially equal volume. Energy from the exothermic pressureoxidation is recovered by heat exchange between the oxidized slurry andacidulated feed to the autoclave. As indicated in FIG. 1, this heatexchange is preferably effected by letting down the pressure of theoxidized slurry in flash tanks in which the nozzles of the currentinvention are used, and using the steam which is flashed from theoxidized slurry to heat the autoclave feed, preferably by direct contactin splash condensers positioned ahead of the autoclave.

After it is partially cooled by flashing of steam, the oxidized slurryis further cooled and then passed directly to a neutralizationoperation. Here lime and/or other base is added to increase the pH toallow for subsequent cyanide leaching. Gold is recovered from theneutralized oxidized slurry by, for example, carbon-in-leach cyanidationin a continuous countercurrent system.

Referring to FIG. 2, ground ore slurry is directed to a trash screen 1;ore slurry passing through the screen is directed to a mechanicalthickening device 2, typically a vertical tank of large diameter whichprovides a net vertical flow low enough to permit sedimentation of thesolid particles. Overflow from the thickener is recycled to the grindingcircuit. Thickened ore slurry underflow from the thickener is directedto another trash screen (not shown) and by a transfer pump 3 to a seriesof stirred acidulation tanks 5, 6 and 7, through which the slurry passescontinuously. Although three stages are shown, in the preferredembodiment there are four stages. A fresh sulfuric acid stream(optional) 4 is added to the acidulation tanks in order to releasecarbon dioxide from the carbonate contained in the slurry, and therebyreduce the equivalent carbon dioxide levels in the ore. To promoteremoval of CO₂, compressed air may be sparged into the acidulationtanks.

Residue slurry leaving the acidulation tanks is fed by a transfer pump 8to the first of a series of brick lined splash condensers 9 and 10, inwhich the treated feed slurry for the pressure oxidation step ispreheated by contact with steam flashed from the oxidized slurry leavingthe pressure oxidation. The successive splash condensers are each,preferably, internally baffled to promote contact between steam andliquid, and are respectively operated at progressively higher pressureand temperature. A 2-stage centrifugal pump 12 is interposed to increasethe pressure of the slurry between condensers.

Pressure oxidation is carried out in an autoclave 15, where the slurryis passed through a plurality of compartments to provide a retentiontime of the order of 50-80 minutes, where it is contacted in thepresence of sulfuric acid with oxygen gas at a temperature of betweenabout 185° and about 225° C., an oxygen partial pressure of at leastabout 25 psig and a total pressure of between about 215 and about 480psig. The final acidity of the slurry leaving the last compartment ofthe autoclave is between 5 and 25 grams sulfuric acid per liter ofsolution, and the final emf of the slurry is between about 480 and about530 mv.

Noncondensables and steam generated during the pressure oxidationoperation are optionally vented through a scrubber. Oxidized slurryleaving the autoclave is passed to a series of flash tanks 17 and 18,through control valves 17 a and 18 a, respectively, and through nozzleassemblies 41 and 42. In the first flash tank the pressure of the slurryis let down from about 420 psig to about 120 psig. In the second flashtank the pressure of the slurry is let down from about 120 psig to aboutatmospheric. Steam from each flash tank is recycled and contacted withautoclave feed slurry in a complementary splash condenser, operated atsubstantially the same pressure as the flash tank, for preheating thefeed slurry. Thus, in the series as illustrated in the drawing, thefirst flash tank 17 is coupled to the last splash condenser 10, and thesecond flash tank 18 is coupled with the first condenser 9.

The flash tanks are vessels of generally cylindrical shape having adished bottom, a dished top, and parallel side walls. As shown in FIG.6, the preferred flash tank has a slurry inlet 49, a steam outlet 48, aslurry outlet 51, a manhole 52 to permit inspection of the tankinterior, a drain 53, and a blank outlet 54.

In the first flash tank, where the slurry pressure is let down fromabout 420 psig to about 120 psig, there is a volume expansion of thesteam of from about 3 to about 3.5 times its volume at 420 psig. In thesecond flash tank, where the slurry pressure is let down from about 120psig to about atmospheric, there is a volume expansion of the steam offrom about 8.5 to about 9.5 times its volume at 120 psig, or on theorder of 30 times its volume at 420 psig. With regard to the secondflash tank, or low pressure flash tank, it is preferred that the totaltank volume be between about 1.6 and about 1.9 times the volume ofslurry it is to hold at any given time. In the preferred embodimentwhere the volume of slurry in the tank is generally maintained betweenabout 9000 and about 10,000 gallons (U.S.), and the volume of the tankis about 16,500 gallons, this helps ensure a slurry depth adequate toreceive and dissipate the energy of slurry as it enters the vessel andimpacts the slurry surface.

Referring to FIG. 3, hot oxidized slurry from the flash tank 18 istransferred to an intermediate agitated storage tank 23. In order tocondition the slurry for gold recovery operations, the temperature ofthe hot oxidized slurry is reduced to about 25 to 40° C. by passing theslurry, by means of pump 24, through a series of shell and tube coolers25. The temperature of the slurry is reduced by exchanging heat from theslurry to a cooling water stream. Cooling water is obtained from arecirculating system in which the water is recycled through a crossflow,induced draft cooling tower 26 by pump 27.

Cooled oxidized slurry which is discharged from the coolers 25 is fedcontinuously through a series of rubber or epoxy lined agitatedneutralization tanks 28, 29 and 30, where it is neutralized with aslurry of lime and/or other base to raise its pH to the neighborhood of10 to 12. Compressed air 34 is optionally sparged into the slurry in theneutralization tanks to convert ferrous iron to ferric iron, as theformer consumes cyanide in the subsequent carbon-in-leach operation. Theneutralized slurry is then directed to a carbon-in-leach operation bytransfer pump 31 where the gold in the oxidized slurry is recovered by,for example, conventional carbon-in-leach (C-I-L) cyanidation.

Turning now to FIGS. 4 and 5 there is shown a prior art nozzle assemblyemployed at location 42 of FIG. 2 from the second (low pressure) flashtank. The assembly consists of a straight choke 60 surrounded by aceramic lined titanium blast tube 61. An impact zone is shown at 62 inFIG. 5 where the blast tube is impacted with steam entrained with oreslurry as it rapidly expands upon entering the flash tank.

FIGS. 6 and 7 show the nozzle of the invention, consisting of first andsecond opposite ends 44 and 45, respectively, and a steam/slurrypassageway 46 extending through the nozzle from the first end 44 to thesecond end 45. The nozzle is constructed from a material having highhardness. One preferred material is a sintered alpha phase siliconcarbide available from Carborundum (Amherst, N. Y.) under the tradedesignation Hexoloy SA.

Slurry and steam pass into the nozzle at the first end 44 and out of thenozzle at the second end 45 thereof to a location inside the flash tank.As shown in FIG. 7, the steam passageway flares outwardly from alocation generally halfway through the passageway, axially inwardly ofthe second end toward the second end. FIG. 6 is a schematicrepresentation—the actual nozzle configuration is more accuratelyportrayed in FIG. 7. In one preferred embodiment, the slurry flow ratethrough the nozzle is between about 100 tons per hour and about 500 tonsper hour of ore slurry comprising between about 30% and about 70% solidsby weight.

Important nozzle dimensions for the prediction and control of flashingbehavior include the straight section or choke diameter, the expansioncone exit diameter, and either the expansion cone length or theexpansion half-angle. By careful selection of these dimensions, it hasbeen discovered that a relationship can be established between pressureupstream of the nozzle and pressure downstream of the nozzle, so thatthe development of shock waves just inside the nozzle exit, whichresulted in excessive noise and vibration with prior designs, andinternal wear can be minimized. In particular, the nozzle is designed sothat the pressure at the discharge end is about the same as the pressurein the tank. The shock waves, noise and vibration are substantiallyreduced in comparison to a system operating under identical conditions(i.e., a “reference” flash tank), with the only difference being use ofa straight choke flash tank nozzle (i.e., a “reference” nozzle). Theshock waves inside the flash tank using the nozzle of the invention areweaker than shock waves inside a flash tank using a straight choke, butotherwise identical. Also, recondensation which occurred as a result ofoverflashing, which recondensation was deleterious to vapor-liquidseparation within the flash tank, thereby causing excessive liquid andsolids entrainment in the recycled steam to the preheat towers, can alsobe minimized.

The choke diameter fixes the slurry mass rate of flow entering the flashtank at a given absolute pressure (or, alternatively, fixes the upstreampressure at a given mass rate of flow) according to the equation:$\overset{.}{m} = {A_{t}\{ {{\frac{v_{fg}}{h_{fg}}\lbrack {( \frac{\partial h}{\partial p} )_{x} - v} \rbrack} - ( \frac{\partial v}{\partial p} )_{x}} \}_{t}^{{- 1}/2}}$

where {dot over (m)} is the mass rate of flow, A_(t) is the chokecross-sectional area, and the remainder of the equation is a uniquefunction of absolute pressure within the choke. A derivation of thisformula is presented below in Appendix A. In one preferred embodimentwhere the pressure is to be let down from between about 140 psia andabout 100 psia to about atmospheric, and where the mass flow rate isfrom about 1500 to about 3000 tons/day solids (50% pulp density), by useof the analysis of the invention, the choke diameter is from about 2.8inches to about 4.6 inches.

The expansion cone exit diameter largely fixes the absolute exitpressure of the flashing slurry upon entering the flash tank. It isimportant for this exit pressure to match closely the pressure withinthe flash tank, for they are generally not equivalent otherwise. In thepreferred embodiment where the pressure is to be let down from betweenabout 140 psia and about 100 psia to about atmospheric, and where themass flow rate is from about 1500 to about 3000 tons/day solids (50%pulp density), by use of the analysis of the invention, the expansioncone exit diameter is from about 7.7 inches to about 11.5 inches. Theexpansion half-angle is between about 22° and about 30° where the chokediameter and expansion cone exit diameter are as described in thispreferred embodiment. As alluded to above, if the exit pressure is toohigh (i.e., the nozzle does not reduce the pressure far enough),underflashing occurs, in which case a significant amount of flashingmust occur beyond the nozzle. This results in a recirculating flowpattern which causes external wear to the nozzle casing. If the exitpressure is too low (i.e., the nozzle reduces the pressure too far),overflashing occurs, in which case a shock wave develops just inside thenozzle exit resulting in excessive noise and vibration, and possiblyinternal wear. Also, the recondensation which must occur as a result ofthe overflashing may be deleterious to vapor-liquid separation withinthe flash tank, thereby causing excessive liquid and solids entrainmentin the recycled steam to the preheat towers.

The expansion cone length fixes the expansion half-angle for any givenset of choke and exit diameters. It is important that the expansion conebe between ten and twenty centimeters (about four and eight inches)long. Shorter than 10 cm, and vapor-liquid equilibrium cannot be assumedduring flashing. Longer than about 20 cm, and friction losses may becomesignificant, thereby invalidating the assumption of isentropic flow.Either of these two situations limits the predictability of flashing,and are therefore to be avoided. Hence, the optimum length of theexpansion cone is taken to be about 15 cm (6 in). In the case of thelow-pressure flash tanks at Barrick Goldstrike, given the necessarychoke and exit diameters, this results in an expansion half-angle ofabout 15°. This angle also has a very slight effect on exit pressure.However, once it is fixed, then the exit diameter may be chosen withconfidence from the mathematical model of slurry flashing.

The graph of FIG. 11 illustrates predicted absolute pressure versuslength within the existing low-pressure flash system at BarrickGoldstrike at the design solids flow rate. This graph shows how thetarget downstream pressure may be obtained within a certain expansioncone length, given a certain expansion half-angle. This graph depictsthe optimum design for the low-pressure flash nozzle, with 8.4 bar (120psi) absolute entrance pressure, and 0.8 bar (12 psi) absolute exitpressure.

Note that the choke section is about 10″ long, and the expansion cone isabout 6″ long. To achieve the desired pressure in this case, theexpansion half-angle must be 32°, more than twice as much as 15°. Inthis sense, the existing Barrick design is a compromise, whichcompromise results in greater pressure at the end of the nozzle, in turnresulting in some degree of explosive flashing, backflow andcorresponding wear at the end of the nozzle. The reason for thecompromise was that a smaller expansion cone exit diameter was necessaryfor the nozzle to fit through the existing hole at the top of the flashtank. In view of this compromise, there is a sacrificial wear collar onthe outside of the nozzle at its end.

Kinetic power due to steam expansion developed within the optimum designat the pressures shown in FIG. 11 is depicted in FIG. 12. Note that thekinetic power developed is only about half of a megawatt. This isapproximately 8 times less than the original choke/blast-tube apparatus(which self-destructed).

In one preferred embodiment of the invention shown in FIG. 7 thestraight section or choke diameter is between about 3½ and about 4½inches, preferably between about 3.8 and 4.1 inches. The expansion coneexit diameter is between about 7 and about 7½ inches, preferably betweenabout 7.1 and 7.4 inches. The expansion cone length is between about 5¾inches and about 6¾ inches, preferably between about 6 and 6.2 inches.The expansion half-angle is between about 12° and about 18°, preferablybetween about 14° and about 16°. The straight section has a length ofbetween about 8 inches and about 12 inches, more preferably betweenabout 9½ inches and about 10½ inches.

EXAMPLE 1

A nozzle as described above and shown in FIG. 7 was made from Hexoloy SAavailable from Carborundum. The nozzle had an inner diameter of 4 inchesin the first upper segment, and upper segment length of 10 inches, alower segment length of 6.1 inches, the lower segment flaring at anangle of 15° from an inner diameter of 4 inches to an inner diameter of7.25 inches. This nozzle was installed in a low pressure flash tank forreducing slurry pressure from about 120 psig to about atmosphericpressure. The nozzle was installed without a blast tube. After 30 weeks,even without a blast tube, no significant wear was visible on the nozzlenor on the flash tank vessel walls.

As various changes could be made in the above embodiments withoutdeparting from the scope of the invention, it is intended that allmatter contained in the above description shall be interpreted asillustrative and not in a limiting sense.

Appendix A

Formulation of the Equations Governing Flashing Flow of Slurries

Model assumptions:

1. Homogeneous flow—vapor, liquid, and solid phases are flowing at thesame velocity at any point within the system.

2. Vapor-liquid equilibrium—flashing occurs via a known thermodynamicpath.

3. Isentropic flow—the slurry loses no energy to friction.

4. Adiabatic flow—the slurry gains no heat, and does no work.

5. Solid-fluid thermal equilibrium—all phases at a uniform temperatureat any point within the system.

Homogeneous flow theory provides the simplest technique for analyzingmultiphase flows, and can be fairly accurate so long as the phases areintimately mixed, which is the case in flashing slurries. The assumptionof vapor-liquid equilibrium is more troublesome. It is known that rapidacceleration and pressure changes render equilibrium theory inaccuratefor describing the discharge of flashing steam-water mixtures throughorifices, making it necessary to consider the rates of bubble nucleationand growth in the superheated liquid. However, controlled expansionthrough nozzles as short as 10 cm can be predicted with surprisingaccuracy.

In flashing flow through nozzles, pressure drops are generally verylarge, and thus friction becomes an insignificant source of entropy.Furthermore, in the absence of heat sources or turbines, the adiabaticassumption can be safely made. Finally, the rate of heat transfer fromfinely ground solids can be safely assumed high enough to ensure thermalequilibrium between the solid and fluid phases.

Derivation of the model equations:

The basic equations for steady one-dimensional homogeneous equilibriumflow in a duct are: $\begin{matrix}{{\text{Continuity:}\quad \overset{.}{m}} = {{\rho \quad {uA}} = {\frac{uA}{v} = \text{constant}}}} & (1) \\{{\text{Momentum:}\quad \overset{.}{m}\frac{u}{z}} = {{{- A}\frac{p}{z}} - {P\tau}_{w} - {{A\rho g}\quad \cos}}} & (2) \\{{{\text{Energy:}\quad \frac{q}{z}} - \frac{w}{z}} = {\overset{.}{m}\frac{}{z}( {h + \frac{u^{2}}{2} + {gz}} )}} & (3)\end{matrix}$

where {dot over (m)} is the slurry mass rate of flow, ρ and v are theslurry density and specific volume, u is velocity, A and P are the ductcross-sectional area and perimeter, τ_(w) is the average wall shearstress, dq/dz and dw/dz are the rate of heat input and work output perunit length of duct, respectively, z is the vertical coordinate, and θis the angle of inclination of the duct to the vertical. Either ρ or 1/vmay be used to express slurry density. For our purposes, v is moreconvenient.

Equation (2) may be rewritten as an explicit equation for the pressuredrop: $\begin{matrix}{{- \frac{p}{z}} = {{\frac{P}{A}\tau_{w}} + {\frac{\overset{.}{m}}{A}\frac{u}{z}} + {\rho \quad g\quad \cos \quad \theta}}} & (5)\end{matrix}$

The three terms on the right side can then be regarded as frictional,accelerational, and gravitational components of the pressure drop:$\begin{matrix}{{- \frac{p}{z}} = {{- ( \frac{p}{z} )_{F}} - ( \frac{p}{z} )_{A} - ( \frac{p}{z} )_{G}}} & (6)\end{matrix}$

In the absence of significant friction losses, and when gravitationaleffects are negligible: $\begin{matrix}{( \frac{p}{z} )_{F} = {( \frac{p}{z} )_{G} = 0}} & (7)\end{matrix}$

and Newton's second law of motion can be stated: $\begin{matrix}{{- \frac{p}{z}} = {{- ( \frac{p}{z} )_{A}} = {\frac{\overset{.}{m}}{A}\frac{u}{z}}}} & (8)\end{matrix}$

Assuming steady flow, and since each phase within the slurry shares thesame velocity (homogeneous flow): $\begin{matrix}{{- \frac{p}{z}} = {G\frac{u}{z}}} & (9)\end{matrix}$

where G is the rate of slurry mass flux, or the slurry mass velocity.Combining equations (1) and (8): $\begin{matrix}{{- \frac{p}{z}} = {G\frac{}{z}( \frac{\overset{.}{m}v}{A} )}} & (10)\end{matrix}$

Expanding this differential: $\begin{matrix}{{- \frac{p}{z}} = {{G^{2}\frac{v}{z}} - {\frac{G^{2}v}{A}\frac{A}{z}}}} & (11)\end{matrix}$

By definition:${{v \equiv {{( {1 - S} )\lfloor {{xv}_{g} + {( {1 - x} )v_{f}}} \rfloor} + {Sv}_{s}}}\therefore\frac{v}{z}} = {( {1 - S} )\lbrack {{v_{fg}\frac{x}{z}} + {x\frac{v_{g}}{z}} + {( {1 - x} )\frac{v_{f}}{z}}} \rbrack}$

where x is the steam quality or mass fraction of the total wateroccurring as steam, S is the pulp density or solids mass fraction withinthe slurry, and the subscripts f, g, fg and s refer to liquid water(fluid), steam (gas), the difference between the two, and solids,respectively. For a vapor-liquid system, specific volume is a uniquefunction of pressure, thus: $\begin{matrix}{\frac{v}{z} = {{( {1 - S} )v_{fg}\frac{x}{z}} + {( \frac{\partial v}{\partial p} )_{x}\frac{p}{z}}}} & (13)\end{matrix}$

where:$( \frac{\partial v}{\partial p} )_{x} = {( {1 - S} )\lfloor {{x\frac{v_{g}}{p}} + {( {1 - x} )\frac{v_{f}}{p}}} \rfloor}$

Typically, the steam quality gradient, dx/dz, may be calculated from theenergy equation by equating heat transfer to latent heat changes.However, if significant flashing occurs, quality is a function of bothenthalpy, h, and pressure, thus: $\begin{matrix}{x = {{{x( {h,p} )}\therefore\frac{x}{z}} = {{( \frac{\partial x}{\partial h} )_{p}\frac{h}{z}} + {( \frac{\partial x}{\partial p} )_{h}\frac{p}{z}}}}} & (15)\end{matrix}$

By definition: $\begin{matrix}{{{h \equiv {{( {1 - S} )\lfloor {{xh}_{g} + {( {1 - x} )h_{f}}} \rfloor} + {Sh}_{s}}}\therefore( \frac{\partial x}{\partial h} )_{p}} = {\frac{1}{( {{\partial h}/{\partial x}} )_{p}} = \frac{1}{( {1 - S} )h_{fg}}}} & (16)\end{matrix}$

Also, by Euler's rule: $\begin{matrix}{( \frac{\partial x}{\partial p} )_{h} = {{{- ( \frac{\partial x}{\partial h} )_{p}}( \frac{\partial h}{\partial p} )_{x}} = {{- \frac{1}{( {1 - S} )h_{fg}}}( \frac{\partial h}{\partial p} )_{x}}}} & (17)\end{matrix}$

where:$( \frac{\partial h}{\partial p} )_{x} = {{( {1 - S} )\lfloor {{x\frac{h_{g}}{p}} + {( {1 - x} )\frac{h_{f}}{p}}} \rfloor} + {{SC}_{ps}\frac{T}{p}}}$

where C_(ps) is the heat capacity of the solids, and the temperature Tis a unique function of pressure from the vapor-liquid equilibrium.Thus, combining equations (13), (14) and (15), the steam qualitygradient is expressed: $\begin{matrix}{\frac{x}{z} = {\frac{1}{( {1 - S} )h_{fg}}\lfloor {\frac{h}{z} - {( \frac{\partial h}{\partial p} )_{x}\frac{p}{z}}} \rfloor}} & (19)\end{matrix}$

and combining this with equation (12) gives the specific volumegradient: $\begin{matrix}{\frac{v}{z} = {{\frac{v_{fg}}{h_{fg}}\quad \frac{h}{z}} + {\lfloor {( \frac{\partial v}{\partial p} )_{x} - {\frac{v_{fg}}{h_{fg}}( \frac{\partial h}{\partial p} )_{x}}} \rfloor \frac{p}{z}}}} & (20)\end{matrix}$

In the absence of a significant potential energy gradient and underadiabatic conditions, equation (2) may be rearranged to solve for theenthalpy gradient: $\begin{matrix}{\frac{h}{z} = {{{{- u}\quad \frac{u}{z}}\therefore\quad {h_{0} \equiv {h + \frac{u^{2}}{2}}}} = {constant}}} & (21)\end{matrix}$

where h₀ is the “stagnation enthalpy.” Combining equations (1), (8), and(18) gives the enthalpy gradient as a function of pressure drop:$\begin{matrix}{\frac{h}{z} = {v\quad \frac{p}{z}}} & (22)\end{matrix}$

which, when combined with equation (17), gives the final expression forthe specific volume gradient: $\begin{matrix}{\frac{v}{z} = {\{ {( \frac{\partial v}{\partial p} )_{x} - {\frac{v_{fg}}{h_{fg}}\lbrack {( \frac{\partial h}{\partial p} )_{x} - v} \rbrack}} \} \frac{p}{z}}} & (23)\end{matrix}$

which, when combined with equation (10), gives the pressure drop as afunction of system operating variables and steam table data only:$\begin{matrix}{{- \frac{p}{z}} = \frac{{- \quad \frac{G^{2}v}{A}}\frac{A}{z}}{1 + {G^{2}\{ {( \frac{\partial v}{\partial p} )_{x} - {\frac{v_{fg}}{h_{fg}}\lbrack {( \frac{\partial h}{\partial p} )_{x} - v} \rbrack}} \}}}} & (24)\end{matrix}$

The choking condition is thus: $\begin{matrix}{M^{2} = {{{- G^{2}}\quad \{ {( \frac{\partial v}{\partial p} )_{x} - {\frac{v_{fg}}{h_{fg}}\lbrack {( \frac{\partial h}{\partial p} )_{x} - v} \rbrack}} \}} = 1}} & (25)\end{matrix}$

where M is the Mach number. Hence, the critical slurry mass rate of flowis determined by: $\begin{matrix}{\overset{.}{m} = {A_{t}\quad \{ {{\frac{v_{fg}}{h_{fg}}\lbrack {( \frac{\partial h}{\partial p} )_{x} - v} \rbrack} - ( \frac{\partial v}{\partial p} )_{x}} \}_{t}^{{- 1}/2}}} & (26)\end{matrix}$

where the subscript t denotes conditions in the “throat” or narrowestsection of the choke. Finally, combining equations (16) and (19) resultsin the final expression for steam quality gradient: $\begin{matrix}{\frac{x}{z} = {\frac{1}{( {1 - S} )h_{fg}}\lfloor {v - ( \frac{\partial h}{\partial p} )_{x}} \rfloor \frac{p}{z}}} & (27)\end{matrix}$

Equations (24) and (27) are the working equations of the model. With agiven choke or nozzle and the steam tables, these two equations may beintergrated numerically to determine the critical slurry mass rate offlow, and the corresponding fluid properties, anywhere in the nozzle.

Quantities of interest for plotting vs length along the nozzle includepressure, stem quality, Mach number, and the rate of kinetic energy, orkinetic power:${\overset{.}{E}}_{K} = {\frac{\overset{.}{m}\quad u^{2}}{2} = \frac{{\overset{.}{m}}^{3}\quad v^{2}}{2A^{2}}}$

What is claimed is:
 1. A wear-resistant flash tank pressure let downnozzle for use in passing an ore slurry into an ore slurry flash tank torelease steam from the slurry and reduce the pressure of the slurry, thenozzle comprising an inlet end, a discharge end, a tubular passagewayextending therebetween for passage of the slurry from a location outsidethe flash tank in fluid flow communication with said inlet end, theslurry passageway comprising a choke comprising a zone of the passagewayin which its cross-sectional area is smallest, the passageway flaringwith respect to the axis thereof toward said discharge end to define anexpansion cone; and the cross-sectional area of the choke and the exitdiameter of the expansion cone being selected to establish arelationship between pressure upstream of the nozzle and pressure in theflash tank so that shock waves inside the flash tank are weaker thanshock waves inside a reference flash tank having identical dimensionsand configuration and operating under identical conditions except havinga reference pressure let down nozzle consisting of a straight choke. 2.The nozzle of claim 1 wherein the cross-sectional area of the choke andthe exit diameter of the expansion cone are selected to establish arelationship between pressure upstream of the nozzle and pressure in theflash tank so that under a flowrate of up to about 500 tons per hour ofore slurry comprising between about 30% and about 70% solids by weight,shock waves inside the flash tank are weaker than shock waves inside areference flash tank having identical dimensions and configuration andoperating under identical conditions except having a reference pressurelet down nozzle consisting of a straight choke.
 3. The nozzle of claim 2wherein the expansion cone has a half angle of between about 20° andabout 32°, and the choke cross-sectional area is determined by afunction relating mass flow rate of slurry through the nozzle andpressure within the nozzle.
 4. A wear-resistant flash tank pressure letdown nozzle for use in passing an ore slurry into an ore slurry flashtank to release steam from the slurry and reduce the pressure of theslurry, the nozzle comprising an inlet end, a discharge end, a tubularpassageway extending therebetween for passage of the slurry from alocation outside the flash tank in fluid flow communication with saidinlet end, the slurry passageway comprising a choke comprising a zone ofthe passageway in which its cross-sectional area is smallest, thepassageway flaring with respect to the axis thereof toward saiddischarge end to define an expansion cone; the cross-sectional area ofthe choke and the exit diameter of the expansion cone being selected toestablish a relationship between pressure upstream of the nozzle andpressure in the flash tank so that shock waves inside the flash tank areweaker than shock waves inside a reference flash tank having identicaldimensions and configuration and operating under identical conditionsexcept having a reference pressure let down nozzle consisting of astraight choke; and wherein the choke has a diameter between about 2.8inches and about 4.6 inches, the expansion cone exit diameter is betweenabout 7.7 inches and about 11.5 inches, and the expansion cone length isbetween about 4 and about 8 inches.
 5. The nozzle of claim 4 wherein theexpansion cone has a half angle of between about 20° and about 32°.
 6. Awear-resistant flash tank pressure let down nozzle for use in passing anore slurry into an ore slurry flash tank to release steam from theslurry and reduce the pressure of the slurry, the nozzle comprising aninlet end, a discharge end, a tubular passageway extending therebetweenfor passage of the slurry from a location outside the flash tank influid flow communication with said inlet end, the slurry passagewaycomprising a choke comprising a zone of the passageway in which itscross-sectional area is smallest, the passageway flaring with respect tothe axis thereof toward said discharge end to define an expansion cone;and the cross-sectional area of the choke and the exit diameter of theexpansion cone being selected to establish a relationship betweenpressure upstream of the nozzle and pressure in the flash tank so thatshock waves inside the flash tank are weaker than shock waves inside areference flash tank having identical dimensions and configuration andoperating under identical conditions except having a reference pressurelet down nozzle consisting of a straight choke; wherein the nozzle has achoke diameter of between about 3½ and about 4½ inches, an expansioncone exit diameter of between about 7 and about 7½ inches, and anexpansion cone length of between about 5¾ inches and about 6¼ inches. 7.The nozzle of claim 6 wherein the expansion cone has a half angle ofbetween about 14° and about 16°.
 8. A process for reducing the pressureof pressure oxidized ore slurry from above about 100 psig to aboutatmospheric, the process comprising passing up to about 500 tons perhour ore slurry comprising between about 30% and about 70% solids byweight through a nozzle into a flash tank, the nozzle disposed on thetop of the flash tank and comprising an inlet end and a discharge end,and a slurry passageway extending through the nozzle from the inlet endto the discharge end for passage of the slurry into the flash tank froma location outside the flash tank, the slurry passageway comprising achoke comprising a zone of the passageway in which its cross-sectionalarea is the smallest, the passageway flaring with respect to the axisthereof toward said discharge end to define an expansion cone, the chokecross-sectional area is determined by a function relating mass flow rateof slurry through the nozzle and pressure within the nozzle, and theexit diameter of the expansion cone being selected to establish arelationship between pressure upstream of the nozzle and pressure in theflash tank so that shock waves inside the flash tank are weaker thanshock waves inside a reference flash tank having identical dimensionsand configuration and operating under identical conditions except havinga reference pressure let down nozzle consisting of a straight choke. 9.A process for reducing the pressure of pressure oxidized ore slurry fromabove about 100 psig to about atmospheric, the process comprisingpassing up to about 500 tons per hour ore slurry comprising betweenabout 30% and about 70% solids by weight through a nozzle into a flashtank, the nozzle disposed on the top of the flash tank and comprising aninlet end and a discharge end, and a slurry passageway extending throughthe nozzle from the inlet end to the discharge end for passage of theslurry into the flash tank from a location outside the flash tank, theslurry passageway comprising a choke comprising a zone of the passagewayin which its cross-sectional area is the smallest, the passagewayflaring with respect to the axis thereof toward said discharge end todefine an expansion cone, the choke cross-sectional area is determinedby a function relating mass flow rate of slurry through the nozzle andpressure within the nozzle, and the exit diameter of the expansion conebeing selected to establish a relationship between pressure upstream ofthe nozzle and pressure in the flash tank so that shock waves inside theflash tank are weaker than shock waves inside a reference flash tankhaving identical dimensions and configuration and operating underidentical conditions except having a reference pressure let down nozzleconsisting of a straight choke; wherein the choke has a diameter betweenabout 2.8 inches and about 4.6 inches, the expansion cone exit diameteris between about 7.7 inches and about 11.5 inches, and the expansioncone length is between about 4 and about 8 inches.
 10. The process ofclaim 9 wherein the expansion cone has a half angle of between about 20°and about 32°.
 11. A process for reducing the pressure of pressureoxidized ore slurry from above about 100 psig to about atmospheric, theprocess comprising passing up to about 500 tons per hour ore slurrycomprising between about 30% and about 70% solids by weight through anozzle into a flash tank, the nozzle disposed on the top of the flashtank and comprising an inlet end and a discharge end, and a slurrypassageway extending through the nozzle from the inlet end to thedischarge end for passage of the slurry into the flash tank from alocation outside the flash tank, the slurry passageway comprising achoke comprising a zone of the passageway in which its cross-sectionalarea is the smallest, the passageway flaring with respect to the axisthereof toward said discharge end to define an expansion cone, the chokecross-sectional area is determined by a function relating mass flow rateof slurry through the nozzle and pressure within the nozzle, and theexit diameter of the expansion cone being selected to establish arelationship between pressure upstream of the nozzle and pressure in theflash tank so that shock waves inside the flash tank are weaker thanshock waves inside a reference flash tank having identical dimensionsand configuration and operating under identical conditions except havinga reference pressure let down nozzle consisting of a straight choke;wherein the nozzle has a choke diameter of between about 3½ and about 4½inches, an expansion cone exit diameter of between about 7 and about 7½inches, and an expansion cone length of between about 5¾ inches andabout 6¼ inches.
 12. The process of claim 11 wherein the expansion conehas a half angle of between about 14° and about 16°.
 13. The process ofclaim 8 wherein the flash tank comprises a vapor outlet for steamgenerated therein and a liquid outlet for cooled slurry, theconfiguration of said tank and the position of said nozzle being suchthat, under slurry flashing conditions: the discharge end of said nozzleis spaced above the level of ore slurry in the tank, and the spacing ofsaid discharge end from said slurry level and the depth of the slurry inthe tank are sufficient to preclude substantial erosion of the bottomwall of the tank by the impact of slurry entering and flashing withinthe tank; the head space above the ore slurry level and the horizontalcross-section of the tank are sufficient for vapor/liquid disengagement;and the depth of said ore slurry is sufficient to provide a liquid sealfor said cooled slurry outlet.
 14. A wear-resistant flash tank pressurelet down nozzle for use in passing an ore slurry into an ore slurryflash tank to release steam from the slurry and reduce the pressure ofthe slurry, the nozzle comprising: an inlet end; an outlet end; atubular passageway extending between the inlet end and the outlet endcomprising a choke consisting of a smallest diameter portion of thepassageway, and an expansion cone defined by the passageway flaring withrespect to the axis thereof toward the outlet end; and the diameter ofthe choke and the exit diameter of the expansion cone being selected toestablish a relationship between pressure upstream of the nozzle andpressure in the flash tank so that shock waves inside the flash tank areweaker than shock waves inside a reference flash tank having identicaldimensions and configuration and operating under identical conditionsexcept having a reference pressure let down nozzle wherein thepassageway is cylindrical from the narrowest portion to the outlet end.15. A wear-resistant flash tank pressure let down nozzle for use inpassing an ore slurry into an ore slurry flash tank to release steamfrom the slurry and reduce the pressure of the slurry, the nozzlecomprising: an inlet end; an outlet end; a tubular passageway extendingbetween the inlet end and the outlet end comprising a choke consistingof a smallest diameter portion of the passageway, and an expansion conedefined by the passageway flaring with respect to the axis thereoftoward the outlet end; and the diameter of the choke and the exitdiameter of the expansion cone being selected to establish arelationship between pressure upstream of the nozzle and pressure in theflash tank so that shock waves inside the flash tank are weaker thanshock waves inside a reference flash tank having identical dimensionsand configuration and operating under identical conditions except havinga reference pressure let down nozzle wherein the passageway iscylindrical from the narrowest portion to the outlet end; wherein thechoke has a diameter between about 2.8 inches and about 4.6 inches, theexpansion cone exit diameter is between about 7.7 inches and about 11.5inches, the expansion cone length is between about 4 and about 8 inches,and the expansion cone has a half angle of between about 20° and about32°.
 16. A wear-resistant flash tank pressure let down nozzle for use inpassing an ore slurry into an ore slurry flash tank to release steamfrom the slurry and reduce the pressure of the slurry, the nozzlecomprising: an inlet end; an outlet end; a tubular passageway extendingbetween the inlet end and the outlet end comprising a choke consistingof a smallest diameter portion of the passageway, and an expansion conedefined by the passageway flaring with respect to the axis thereoftoward the outlet end; and the diameter of the choke and the exitdiameter of the expansion cone being selected to establish arelationship between pressure upstream of the nozzle and pressure in theflash tank so that shock waves inside the flash tank are weaker thanshock waves inside a reference flash tank having identical dimensionsand configuration and operating under identical conditions except havinga reference pressure let down nozzle wherein the passageway iscylindrical from the narrowest portion to the outlet end; wherein thenozzle has a choke diameter of between about 3½ and about 4½ inches, theexpansion cone exit diameter is between about 7 and about 7½ inches, theexpansion cone length is between about 5¾ inches and about 6¼ inches,and the expansion cone has a half angle of between about 14° and about16°.
 17. A wear-resistant flash tank pressure let down nozzle for use inpassing an ore slurry into an ore slurry flash tank to release steamfrom the slurry and reduce the pressure of the slurry, the nozzlecomprising: an inlet end; an outlet end; a tubular passageway extendingbetween the inlet end and the outlet end comprising a choke consistingof a smallest diameter portion of the passageway, and an expansion conedefined by the passageway flaring with respect to the axis thereoftoward the outlet end; the diameter of the choke being determined by themass flow rate of the slurry through the nozzle and pressure within thenozzle; and the exit diameter of the expansion cone being selected sothat the pressure of the slurry at the outlet end is about the same asthe pressure in the flash tank.
 18. A wear-resistant flash tank pressurelet down nozzle for use in passing an ore slurry into an ore slurryflash tank to release steam from the slurry and reduce the pressure ofthe slurry, the nozzle comprising: an inlet end; an outlet end; atubular passageway extending between the inlet end and the outlet endcomprising a choke consisting of a smallest diameter portion of thepassageway, and an expansion cone defined by the passageway flaring withrespect to the axis thereof toward the outlet end; the diameter of thechoke being determined by the mass flow rate of the slurry through thenozzle and pressure within the nozzle; and the exit diameter of theexpansion cone being selected so that the pressure of the slurry at theoutlet end is about the same as the pressure in the flash tank; whereinthe choke has a diameter between about 2.8 inches and about 4.6 inches,the expansion cone exit diameter is between about 7.7 inches and about11.5 inches, the expansion cone length is between about 4 and about 8inches, and the expansion cone has a half angle of between about 20° andabout 32°.
 19. A wear-resistant flash tank pressure let down nozzle foruse in passing an ore slurry into an ore slurry flash tank to releasesteam from the slurry and reduce the pressure of the slurry, the nozzlecomprising: an inlet end; an outlet end; a tubular passageway extendingbetween the inlet end and the outlet end comprising a choke consistingof a smallest diameter portion of the passageway, and an expansion conedefined by the passageway flaring with respect to the axis thereoftoward the outlet end; the diameter of the choke being determined by themass flow rate of the slurry through the nozzle and pressure within thenozzle; and the exit diameter of the expansion cone being selected sothat the pressure of the slurry at the outlet end is about the same asthe pressure in the flash tank; wherein the nozzle has a choke diameterof between about 3½ and about 4½ inches, the expansion cone exitdiameter is between about 7 and about 7½ inches, the expansion conelength is between about 5¾ inches and about 6¼ inches, and the expansioncone has a half angle of between about 14° and about 16°.